How to play Calcudoku
Calcudoku is a number puzzle that mixes Sudoku with simple sums. Fill the grid so each row and column has every number once, and make the numbers in each outlined cage reach the target using the sign shown. The sums are easy; the fun is in the logic.
Step by step
Know the numbers
A 4 by 4 grid uses 1 to 4, a 6 by 6 grid uses 1 to 6, and so on.
No repeats in a line
Each number appears exactly once in every row and every column.
Read the cages
Thick lines mark groups of squares called cages. Each cage shows a target number and a sign.
Hit the target
The numbers in a cage must make the target using the sign: add, take away, multiply or divide.
Fill single squares first
A cage of one square just shows its number. Write it in straight away.
Use logic to finish
Combine the cage sums with the no-repeat rule until every square is filled.
The full rules
What you need
Calcudoku is played on a square grid. Small puzzles are 3 by 3 or 4 by 4; larger ones go up to 9 by 9. The grid is divided by thick lines into cages, groups of one or more squares. Each cage has a small clue in its top corner, such as 6+ or 2÷.
The rules
- Use the right numbers. On a 4 by 4 grid, use the numbers 1 to 4. On a 6 by 6 grid, use 1 to 6.
- No repeats in rows or columns. Each number appears exactly once in every row and every column.
- Make the cage targets. The numbers in each cage must combine to make the target, using the sign shown:
- + add them together,
- − take the smaller from the larger,
- × multiply them together,
- ÷ divide the larger by the smaller.
A cage of a single square shows just a number. That is the number in the square.
Numbers may repeat inside a cage, as long as they are not in the same row or column.
A small example
Imagine a 4 by 4 grid with a cage of two squares side by side marked 7+. The two numbers must add to 7. Using 1 to 4, the only choice is 3 and 4. You do not yet know which way round, but you know no other 3 or 4 can go in that row.
A cage marked 3− with two squares must hold 1 and 4, because 4 take away 1 is the only way to make 3.
Getting started
- Fill single-square cages first. They are given to you.
- Look for cages with only one possibility. For example, on a 4 by 4 grid, 12× across two squares must be 3 and 4, and 2÷ could be 1 and 2 or 2 and 4.
- Use the no-repeat rule. Once you place a number, cross it off as an option for the rest of its row and column.
- Use pencil marks. Write small notes of the possible numbers in each square.
Winning
The puzzle is solved when every square is filled, every row and column has each number once, and every cage reaches its target. A well-made puzzle has only one solution.
Common variants
- Some puzzles hide the signs, so you must work out whether each cage adds, multiplies and so on.
- Killer Sudoku is a similar idea built on a full Sudoku grid, using only adding.
- Some puzzles use 0 or larger ranges of numbers for an extra challenge.
Tips for beginners
- Start with 4 by 4 grids. They teach the method quickly.
- List the options. For each cage, write down the few pairs or triples that could work.
- Look at whole rows. On a 4 by 4 grid, every row adds up to 10. If you know three squares, the fourth follows.
- Look for 5s and 7s. On grids up to 9 by 9, if a × target can be divided by 5, one of its squares must be 5. The same goes for 7.
- Check both directions. Each placement affects its row, its column and its cage.
Common questions
Is Calcudoku the same as Mathdoku?
Yes. The same puzzle is called Calcudoku, Mathdoku, maths Sudoku and several other names.
Can a number repeat inside a cage?
Yes, as long as the repeated numbers are not in the same row or column. This often happens in L-shaped cages.
How do take-away and divide cages work?
They always have two squares. Take the smaller number from the larger, or divide the larger by the smaller. The order of the squares does not matter.
Do I need to be good at maths?
Only simple sums are needed, and small grids use small numbers. Most of the puzzle is logic, like Sudoku.
Is there a box rule, like in Sudoku?
No. Unlike Sudoku, Calcudoku has no 3 by 3 boxes. Only rows, columns and cages matter.
Where it comes from
Puzzles of this kind are thought to have been devised in Japan in the early 2000s by a teacher, as a way to practise arithmetic and logic. They spread to newspapers and puzzle books around the world in the following years. Because the original name is protected, the puzzle is often published under other names such as Calcudoku or Mathdoku.
